**Question:**

*True/False?*

There exists a continuous surjective map from the complex plane onto the non-zero reals.

*Hint:*

Search for topological invariants.

**Discussion:**

Under a continuous function, connected set must go to connected set. The complex plane (\mathbb{C}) is connected.

It’s image must be connected.

(\mathbb{R}-0) is not connected.

So the statement is *False*.

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